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Number of partitions of n into distinct parts that contain primes to odd powers only (A002035).
1

%I #4 Jul 29 2017 19:28:06

%S 1,0,1,1,0,2,1,2,3,2,4,4,3,7,5,8,9,9,12,12,14,18,18,22,27,25,34,34,39,

%T 47,49,57,67,67,83,88,96,115,119,139,154,165,190,206,224,259,273,311,

%U 341,367,415,447,490,550,588,654,720,771,862,928,1013,1121,1204,1324,1448,1554,1716,1850,2008,2203,2366

%N Number of partitions of n into distinct parts that contain primes to odd powers only (A002035).

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} (1 + x^A002035(k)).

%e a(8) = 3 because we have [8], [6, 2] and [5, 3].

%t nmax = 70; CoefficientList[Series[Product[1 + Boole[And @@ OddQ /@ FactorInteger[k][[All, 2]]] x^k, {k, 2, nmax}], {x, 0, nmax}], x]

%Y Cf. A002035, A290369.

%K nonn

%O 0,6

%A _Ilya Gutkovskiy_, Jul 28 2017